Councils have said the government is failing to release funds to improve the fire safety of dozens of tower blocks following the Grenfell Tower disaster despite promising that a lack of financial resources should not stand in the way of essential works.

Ministers have said building owners are responsible for funding safety measures, but town hall leaders complain that they are “washing their hands of their responsibilities” and are being “dismissive”, four months after the blaze at the Kensington tower block, which claimed about 80 lives.

The government has said it will consider help “where works are essential”, but has so far resisted bids for support to retrofit sprinklers in towers despite the London fire brigade (LFB) saying this must happen.

The Conservative-run Westminster council is understood to be the latest town hall to have had a request for financial assistance pushed back by ministers. It is removing cladding from six high-rise towers and wants to install sprinklers across other tall council blocks at an estimated cost of £20m.

The housing minister, Alok Sharma, has already declined Nottingham city council’s request for help to install sprinklers inside flats and communal areas in 13 towers at a cost of £6.2m. Sharma told the council: “The fire safety measures you outline are additional rather than essential.”

He has told the London borough of Croydon, which wants to spend £10m on retrofitting sprinklers to 25 tall residential blocks: “It is the landlord’s responsibility to ensure that people are safe.”

Wandsworth wants to spend up to £30m on sprinklers in 100 towers but has been told: “Support will not include general improvement and enhancements to buildings.” All the councils said they had been advised to carry out works by their local fire brigades.

The tension over who should foot the fire safety bill follows a pledge in July by the communities secretary, Sajid Javid, that any lack of financial resources would not prevent necessary works going ahead. However, the government appears determined not to fund or allow additional borrowing for any improvements that go beyond essential safety works. The necessity of sprinklers is proving a key faultline.

Dany Cotton, commissioner of the LFB, has said retrofitting sprinklers in tower blocks “can’t be optional, it can’t be a nice-to-have”. Since 2007 they have been compulsory in new-build high-rises over 30 metres tall in England, but those building regulations do not apply to older blocks.

The Department for Communities and Local Government (DCLG) argues that an appropriate level of fire safety can be achieved without the need to retrofit sprinklers, and fitting them is a matter for landlords to consider for themselves.

A recent study of 677 fires where sprinklers were activated found they controlled or extinguished the fire in 99% of cases.

The nationwide bill for replacing flammable cladding and retrofitting sprinklers is already likely to run into hundreds of millions of pounds. Southwark has previously estimated that the bill for installing sprinklers in its towers could be as high as £100m, and it is currently finalising its bid for funding. The council leader, Peter John, has told Javid: “Fire safety is a national issue and the financial burden for these works must not fall on already stretched councils.”

Birmingham city council, the UK’s largest council landlord, is yet to submit a request for retrofitting sprinklers in up to 213 blocks.

So far, 31 town halls have asked for government help to make high-rise flats safe. The DCLG said it was in detailed discussions with six, and others had been invited to provide further information about how the work they wished to undertake was essential.

In Salford, the city council has borrowed £25m to fund works to remove potentially flammable cladding from nine towers, and leaders have accused the government of “failing to live up to its responsibility”.

“Like many other councils, Salford is lobbying the government to recognise the huge financial cost of this national issue and provide funding to us and other local authorities to deal with it,” said the deputy city mayor, John Merry.

Pressed on funding at the Conservative party conference in Manchester this week, Theresa May said: “We have said we would work with local authorities on any adaptations and changes they needed to make to ensure the safety of those tower blocks.”

But asked about funding sprinklers, she said: “There’s a number of issues that can improve the safety of tower blocks. It is not just one answer.”

Jane Urquart, the cabinet member for housing at Nottingham city council, said: “The government said a lot of things after the tragedy about money not being an object to ensuring safety. Now councils like ours, which have faced huge cuts over the last few years, are being told to dig into our pockets. The consequence of the government not paying is that other repairs to our housing stock won’t happen.”

Adam Hug, leader of the Labour opposition at Westminster city council, said he had seen correspondence with the government detailing the council’s request for financial aid or better flexibility on borrowing.

“Both were being asked for,” he said. “They were told: only in exceptional circumstances. Yet again it will be council tenants and people who desperately need new homes who are left to pay the price of this Tory government washing their hands of their responsibilities.”

A spokeswoman for Westminster said it was “in ongoing discussions with the DCLG about a range of fire safety-related issues”. The DCLG said it had told Westminster it would consider removing financial restrictions where barriers stood in the way of essential works being done.

“Building owners are responsible for funding measures designed to make a building safe,” said a spokesman for the department. “We’ve been clear that where a local authority has concerns about funding essential fire safety measures, they should contact DCLG as soon as possible to discuss their position. The department has written to Nottingham, Croydon and Wandsworth councils inviting them to provide more detail about the works they propose. To date these authorities have not submitted this information.”